ode45 or bvp4c? Which one suits this scenario? Please anyone reply

I have a set of differential equations (dPi/dz) for power say for P1 to P7. I have initial power values for P1 to P4 at z=0 and initial power values for P5 to P7 at z= 8. Can I solve this as ode45 or bvp4c?

Because the initial power values I have are not really like boundary conditions. But then how can I use ode45 by using the same P vector definition to have intial values defined for P1 to P4 at one z and for P5 to P7 at another z, as stated above?

[Jan]

What does this mean: "the initial power values I have are not really like boundary conditions"?

Initial values are boundary conditions by definition.

[Jaya]

Of course, they are defined at boundaries but what I mean is (in the following code) isn't it like I define all P1 to P7 at z=0 whereas what I want is signal powers P1 to P4 defined at z=0 but pump powers P5 to P7 alone defined at z=80. But how to let the ode45 know that?

I use the same p vector to do the function definition in lorenz i.e. p(1) to refers to signal 1 power and p(5) refers to pump 1 power. OR is there any totally different way to do this?

 zspan = [0:80]
 p0= -3.5* ones(4,1)   %for P1,P2,P3,P4
  pp1=-300e-3 ; pp2=-310e-3 ; pp3=-320e-3 ;   %for P5, P6, P7
 p_in=[p0;pp1;pp2]   %to form the intial p vector for ode45
 [z,p]= ode45(@lorenz,zspan,p_in)

[John D'Errico]

Please don't keep asking the same question.

Use a boundary value solver, NOT ODE45. However, using a shooting method, as Jan points out, you can use ODE45.

[Jaya]

OK, thanks. But I hope you have observed the no. of days elapsed between my two questions. I read other stuff too and wanted to ask more specifically since I had implemented and again faced problems. I did not ask repetitively without trying. And I myself wrote why I am asking again in my second question. Thanks.

Answer 1

[Jan]

If some conditions are defined at different time points, the problem is not an "initial value problem", which can be solved by ODE45, but a boundary value problem, for which BVP4C or BVP5C is a suitable solver.

An alternative is to write your own boundary value solver:

Start with a smart guess of the missing components of the initial value and integrate with ODE45. You get a difference between the final values and the boundary values at this time point. Then vary the initial conditions to find out the sensitivity. This can be applied with a Newton method to modify the initial values until the final values are matched. This is the "single shooting method".